1. Field
This invention relates to the processing of synthetic aperture radar data and, in particular, to the processing of three dimensional bistatic synthetic aperture radar data.
2. Prior Art
In early radar systems, fine range resolution was obtained by transmitting a narrow pulse, while fine azimuth resolution was obtained by radiating a narrow beam. In more modern radars, pulse compression techniques or active linear FM techniques, commonly referred to as Stretch techniques, are used to produce a long pulse which can, through appropriate processing, provide the range resolution of a narrow pulse.
For example, in the Stretch technique, a linear FM signal is transmitted. The return signal is mixed with a sample of the transmitted signal to produce an output signal at a frequency which is dependent on the range of the target. The range resolution in the Stretch technique is a function of the bandwidth of the transmitted linear FM signal, or alternatively, the resolution may be considered dependent on the range to frequency scale factor and the degree to which the frequency of the output signal for a particular target can be ascertained.
A narrow beamwidth was previously obtained through the use of a large antenna; however, in a more modern technique known as synthetic aperture radar, or SAR, a small antenna can provide the effective aperture of a large antenna. This is accomplished by moving the antenna along a path, the length of which determines the synthetic aperture within the limitation imposed by the antenna beamwidth. The data received along the path is stored and later processed to produce a high resolution image. Conventional SAR radar and its processing are discussed in a number of publications, including The Radar Handbook, by M. Skolnik, McGraw-Hill, New York 1970.
A simple Stretch system is shown in FIG. 1. A transmitter 11 generates a linear FM signal which is passed through a coupler 12, to a first antenna 13, where it is radiated. The radiated signal is returned by a target 15 to a second antenna 14, where it is passed to a mixer 16. The mixer also receives a portion of the transmitted signal by way of the coupler 12 to serve as a local oscillator signal. The mixer output signal, at port 17, often is converted to range information at port 19 by a Fourier transformer 18, which is usually a pulse compression network, also referred to as a matched filter. A matched filter is a more general term, however, including any system for converting received radar signals to Stretch type frequency response signals.
The operation of the system of FIG. 1 can be understood with the aid of FIG. 2. FIG. 2 is a graph containing a plot of a transmitted signal 24, a received signal 25, and an output signal 26. The ordinate 22 represents frequency while the abscissa 23 represents time. The frequency axis is divided in two, with the upper portion being the normalized transmitted frequency, while the lower portion is the output frequency, which is calibrated in megahertz (MHz).
FIG. 2 is an example of the performance characteristics of a typical Stretch system. The transmitted signal varies linearly from 0.8 to 1.2 times the center frequency over a normalized period, while the received signal varies over the same frequency range, but is shown delayed by a time corresponding to the time for the signal to traverse the round trip radar path length to the target and back to the receiver. When these two signals mix in the mixer 16, shown in FIG. 1, they produce a constant low output frequency such as a 4 MHz signal designated by drawing numeral 26, in FIG. 2.
The frequency difference between the transmitted and return signals is proportional to the delay which, in turn, is proportional to the target range. Therefore, an output signal representing a target at a fixed range will be at a frequency that is proportional to the range of the target. In a practical Stretch system, the mixer reference signal obtained via coupler 12 may be delayed a known amount to establish a reference range. The output signal for a target at that range will then be zero frequency.
A rudimentary SAR system is shown in FIG. 3. In this Figure, antennas 31, 32, and 33 produce antenna patterns 34, 35, and 36, respectively, illuminating a target 37.
The antenna and antenna patterns shown in FIG. 3 may be considered a simple phased array antenna system. The signals from each antenna may be phase shifted, weighted and then combined with the signals from the other antennas to produce an effective pattern 39, which is narrower and higher in gain than any of the individual antennas. The narrow beamwidth of the effective pattern may then be used for improved angle resolution.
A SAR system is, in effect, a special case of a phased array system. Although a SAR system usually contains only a single antenna, this antenna is moved to simulate a number of antennas. For example, a single antenna of a SAR system could first be positioned at the location of antenna 31. In this location, it would produce a pattern similar to pattern 34. The signal received at this location containing target information is stored. The single SAR antenna is then moved to the location of antenna 32 and later to that of antenna 33 with the received data at each location being stored. The stored data is then weighted, phase shifted and combined to provide the same results which would have been obtained with three separate antennas.
In practical applications, the single SAR antenna is often located aboard an aircraft. The antenna is continually in motion rather than being shifted in incremental fashion from position to position; however, the transmission period is relatively short, making the distance moved per transmission period equally short. In this case, each transmission may be considered as occurring at a single location.
FIG. 8 illustrates the operation of a typical SAR in an aircraft 81, flying along a flight path 86. The SAR antenna is directed constantly to the side of the aircraft, as shown by directional arrows, such as arrow 82. The radar beam 84 illuminates a swath on the ground 83 and at a particular instant illuminates an area, such as area 85.
A commonly used method for recording SAR data is to print the data on photographic film, such as on the film shown in FIG. 4, using intensity modulation. In this Figure, a film 41 contains a series of lines, such as lines 42 and 43. Each line contains data received as a result of a single transmitted pulse. If Stretch is combined with SAR the peaks of the sinousoidal return signals are recorded as short, dark portions along the line.
FIG. 9A shows the coverage by a SAR radar of two targets. The radar beamwidth 91 illuminates two targets, 93 and 94, in an area of illumination on the ground indicated by the swath 95 of width 92. When the signals from the targets are recorded on film 99 via a series of range sweeps, such as range sweep 96, they appear as shown in FIG. 9B, where signal history 98 corresponds to target 94 and signal history 97 corresponds to target 93. The target histories are curved and cannot be both correct by simple geometric manipulation.
For a Stretch SAR, a single target at a constant range would produce a single frequency, such as the 4 MHz signal illustrated in FIG. 2. This type of return signal would simply produce a series of constant size dots separated by a constant spacing. The dots correspond to the peaks of a 4 MHz signal. A return signal produced by a number of targets generates a more complex darkening of the line.
The data may be recorded on the film simply by displaying the received signal on an oscilloscope and focusing the display on the film. In such a system, the sweep speed corresponds to the rate at which the return signal is printed while the separation between the raster lines corresponds to the distance the antenna travels between pulses.
The data recorded in this form is in terms of frequency and time of receipt, rather than the more conventional target intensity and range. Obtaining the SAR Stretch data in more conventional form requires conversion of the frequency information in the vertical direction to range information. This function may be carried out in analogue fashion by means of a device such as a spectrum analyzer. It also may be carried out in digital fashion by means of a Fourier transform in the vertical direction. To complete the conversion from darkened lines to an image, the data must also be weighted, phase shifted, and properly combined in the horizontal direction.
An improved form of SAR referred to as Spotlight, differs from standard SAR in that the antenna is directed at a single target area, while the antenna is moved along the flight path. The data is also preprocessed by subtracting the Doppler of a reference target in the area, to simplify subsequent data combining. As long as the target area is illuminated, the path length becomes the synthetic aperture for this target. The synthetic aperture, therefore, is not limited by the beamwidth as is the case with a conventional SAR. Furthermore, data combining can now be performed approximately by horizontal Fourier transform.
The data from a Stretch-Spotlight SAR can be corrected so that data combining can be performed exactly with a horizontal Fourier transform, by using a fourth technique known as polar formatting.
FIG. 6 illustrates a Spotlight radar. In this Figure, an aircraft 60 is shown at three positions, 61, 62, 63, along a flight path, indicated by direction arrows 68 and 69. At each point along the flight path, the radar beam is directed at a target 67. The radar beam for positions 61, 62, and 63, is illustrated by beams 64, 65, and 66. Since the angle of the antenna with respect to the flight path is continually changing along the path, the data should not be recorded in the simple straight line fashion, shown in FIG. 4. To correct for the constant change in angle, the data is recorded in polar format, such as that shown in FIG. 7. In this Figure, data lines, such as lines 72 and 73, are recorded on a film 71 in polar coordinates.
It is fortunate that a simple means of providing a complete conversion of Stretch-Spotlight data to an image is available. The data in the form shown in FIG. 7 may be converted directly to an image by means of a spherical lens. This process is shown pictorially in FIG. 5. In this Figure, a reflector 51 directs light from a light source 52 through a columnating lens 53. The columnated light 54 passes through a film 55 containing the record data. The light emerging from the film is then passed through a spherical lens 56 to where the light rays 57 are converged produce an image on the screen or second film 58. This simple, complete conversion only works exactly on Stretch-Spotlight polar formatted monostatic SAR data.
In the SAR systems described above, it is assumed that the transmitter and receiver are located on board the same platform, such as aboard a single aircraft. This type of system is referred to as a monostatic imaging radar system. It is advantageous in some applications to place the transmitter aboard one platform and the receiver aboard another. This type of system is referred to as a bistatic imaging radar system. A serious problem arises in properly recording the received data from a bistatic system so that an image may be produced by the relatively simple Fourier transform method similar to that shown in FIG. 5.
Bistatic radar presents fundamental geometric processing problems which are similar in some respects, to those encountered in monostatic SAR technology. These geometric problems arise from target motion through resolution cells and are, in fact, a direct result of the geometric motion of what is referred to as the iso-Doppler and iso-range lines of the bistatic radar system during the interval required to collect the data for image formation. In particular, for most bistatic geometries, the iso-Doppler and iso-range lines are not perpendicular and, if this data is processed conventionally, it will result in a skewed image, such as an square object being imaged as a parallelogram. Furthermore, since the image skewing varies with time, changes in the skew of the parallelogram will limit the resolution that can be achieved.
Iso-Doppler and iso-range lines for a monostatic SAR system are shown in FIG. 10. In this Figure, an aircraft 101 carrying a SAR is moving at a velocity V.sub.a 103. The vector V.sub.a is the relative velocity with respect to the aircraft of a target directly ahead. The SAR may be considered the center of a series of concentric spheres, such as sphere 102, which represents a constant range from the SAR. Where these spheres intersect a plane, such as the earth surface, they produce circles which are referred to as iso-range lines.
FIG. 17 shows the transmitter circling the field of view. The transmitter starts at angle 1 designated by drawing numeral 1701 and fly along flightpath 1706 to angle 21702, angle 41704, angle 31730, and finally, back to angle 1. The FOV is 1707 containing illustrative targets A 1708, C 1709 and B 1710. FIG. 18 is a superposition FIG. 17 of the iso-Doppler and iso-range lines with the transmitter at angle 2 which is designated 1802 in FIG. 18.
All targets along a line emanating from the SAR have at one instant in time, a constant relative velocity toward the SAR. For example, targets 105 and 108 on line 106 have a relative velocity of V.sub.R, represented by vector 104, towards the SAR. These targets will produce the same Doppler frequency because of their same relative velocity towards the SAR and therefore the line 106 is referred to as an iso-Doppler line.
All targets on lines making the same angle with the aircraft velocity vector, V.sub.a will have the same property because they will all have the same relative velocity V.sub.R towards the SAR. These lines form a cone. Lines 106 and 107 represent the intersection of the cone with a plane, such as the earth's surface.
An infinite number of cones are possible. For example, lines 110 and 111 represent the intersection of another iso-Doppler cone with the earth surface. For clarity we will begin with such a description in two dimensions. The concept will be extended later into three dimensions.
Conventionally, a sharp gradient in iso-Doppler lines is represented by a high density of lines, while the direction of the gradient is taken as being perpendicular to the iso-Doppler lines. A similar representation is used for iso-range lines.
Note that in the monostatic system depicted in FIG. 10, the iso-doppler lines are radial and therefore intersect the iso-range circles at right angles. As will be shown, the configuration of iso-range and iso-Doppler lines in most instances is quite different for bistatic radar.
FIG. 12 shows the change in iso-Doppler and iso-range lines as the transmitter position is changed. The transmitting aircraft 1201 is shown prior to crossing the flightpath of the receiving aircraft's 1202 in FIG. 12A, while the transmitting aircraft is shown after having crossed the receiving aircraft's flightpath in FIG. 12B. Idealized iso-Doppler and iso-range lines 1204 are shown within the field of view 1203. Actual iso-range lines are perpendicular to the bistatic angle bisector, while actual iso-Doppler lines are parallel to the lines 1205 or 1206.
The central problem in bistatic radar is target location. It is necessary to determine how range delay and Doppler shift relates to target position.
To simplify the discussion, it will be assumed that a Stretch system will be used throughout and in this Stretch system the definition of range delay is the relative time between the received signal from the target and the signal from a reference point of known position. This approach requires the least knowledge of transmitter and receiver positions.
It also will be assumed that a Spotlight system will be used throughout and in such a system a Doppler shift in bistatic radar is due to the movement of both the transmitter and receiver. Doppler will be taken with respect to a reference point, which is usually located within the field of view. The Doppler at this point will be set to zero; that is, the Doppler at the reference point will be subtracted from the Doppler at all other points in the field of view.
Referring to FIG. 11, to simplify the description, it sill first be assumed that in FIG. 11A the receiver aircraft 1103 is always directed toward the field of view 1104 so it appears nonrotating by an observer 1110 located in the field of view, while the transmitter 1101 is always broadside to the field of view, so it appears to be rotating.
In FIG. 11B, the receiver aircraft 1107 is shown flying on a path parallel to the transmitter aircraft 1105. The receiver aircraft is still directed towards the field of view 1109 so it appears nonrotating by an observer 1111 located in the field of view, while the transmitter aircraft 1105 remains broadside to the field of view so that it appears to rotate.
In order to understand the purpose of the present invention it is necessary to compare the iso-Doppler and iso-range line configurations for monostatic and bistatic radar. First note that the position of the nonrotating, receiving aircraft does not influence the position of the iso-Doppler lines.
The reason the receiving aircraft does not produce a Doppler gradient is explained with the aid of FIGS. 13A and 13B. In FIG. 13A, a receiving aircraft 1301 is shown approaching a field of view 1303 which contains two targets 1304 and 1305. The angle that target 1304 makes with the line of flight 1302 is designated .phi..
Since the receiving aircraft is almost directly approaching the target 1304, its Doppler is high; however, there is little change in the Doppler throughout the approach because the target 1304 essentially remains directly ahead and the aircraft remains at a constant velocity.
On the other hand, if the field of view were shifted to another target off to the side, such as target 1307, the Doppler due this target would change at the same rate as the velocity component of the aircraft toward the target.
FIG. 13B is a graph of the Doppler with respect to the angle .phi.. In this Figure, the ordinate 1308 is the magnitude of the Doppler shift while the abscissa is the angle .phi.. The plot 1309 is a cosine function, which corresponds to the component of velocity towards a target at an angle .phi. from the aircraft. It can be seen from this graph that, although the highest absolute Doppler value is produced where .phi. is equal to zero, the greatest rate of change is produced where .phi. is 90 degrees. Therefore, for this simplified example the receiving aircraft with .phi. nearly equal to zero introduces a large Doppler shift to all targets in the field of view, but produces little change in the Doppler shift. Consequently, the receiving aircraft does not influence the position of the iso-Doppler lines, whereas the transmitting aircraft, with a value of .phi. of nearly 90 degrees, produces virtually all the change in Doppler across the field of view and essentially establishes the iso-Doppler lines.
Since the transmitter aircraft is the only aircraft producing the iso-Doppler lines, they will be radial lines drawn from the transmitter to a target and as the aircraft moves, these lines will rotate about the target.
The direction of the iso-range lines in the target area will also rotate, but not at the same rate as the iso-Doppler lines. This can be seen with the aid of FIG. 14.
In this Figure, a transmitter 1401 and a receiver 1402 form the foci for a series of eliptical iso-range lines 1408. A target 1403 is shown located on one of the iso-range lines. An angle .theta., referred to as the bistatic angle, is located at the target and is defined by lines 1404 and 1405 drawn from the target to the transmitter and a receiver, respectively. Line 1407 is the angle bisector of the bistatic angle.
By definition, all targets which produce signals that arrive at the receiver at the same time are located on an iso-range line. For a signal to arrive at the same time as another signal, its total path length from the transmitter to a target and then to the receiver, must be the same, or the sum of the length of line 1404 and 1405 must be a constant. A constant sum for these two line lengths is one definition of an ellipse and accordingly explains the elliptical contours of the iso-range lines for the bistatic case.
The line 1404 is an iso-Doppler line as it connects the transmitter with the target. The angle of the iso-Doppler line may be taken with respect to any reference line, such as the line 1405. If the line 1405 is chosen, then the angle of the iso-Doppler line 1404 is equal to the bistatic angle.
If in FIG. 14 it is assumed that the transmitter is moved on any flight path, except the one directed toward target 1403, the bistatic angle will change, as will the angle of the iso-Doppler line. The direction of the iso-range line, which is the tangent to the iso-range ellipse at the target, is perpendicular to the bistatic angle bisector 1407. The direction of the iso-range lines in the target area therefore changes with the angle bisector 1407.
As long as the receiver is either stationary or moves toward or away from the target 1403, the change in the angle of the iso-Doppler lines can be taken as being equal to the change in bistatic angle, while the change in the direction of the iso-range lines is equal to the change in one-half the bistatic angle.
If in the general case, both receiver and transmitter rotate about the field of view, the iso-range lines behave in the same way, however, the iso-Doppler lines are affected by the receiver rotation. In the extreme case in which the transmitter and receiver rotate at the same rate and direction about the field of view, the iso-range lines remain perpendicular to the bistatic angle bisector, but the iso-Doppler lines become parallel to the bistatic angle bisector, and therefore, remain perpendicular to the iso-range lines at all time. Thus in the extreme, no change in monostatic polar processing is required, as the bistatic system behaves monostatically. The intermediary cases can be considered as a combination of the present invention with conventional polar format processing.
Returning now to the simple example of the non-rotating receiving station, the initial orientation of the iso-Doppler and iso-range lines in the field of view for the bistatic case is generally not orthogonal except for the special case when both the aircraft and target are on the same straight line; however, it might be possible to correct for the skewed image caused by the lack of orthogonality by conventional topographical image reconstitution techniques if the bistatic angle changes only a small amount over the synthetic aperture.
Since the direction of the iso-Doppler and iso-range lines change at different rates, it would also be possible to make some additional correction in processing the recorded data for larger bistatic angle changes by, in effect, rotating the data at a speed halfway between the rate of change in the direction of the iso-Doppler lines and the iso-range lines. The improvement provided by this correction is obviously limited because neither the rotation of the iso-Doppler nor that of the iso-range lines is completely corrected.
Also note from FIG. 14 that increase of the bistatic angle 1406 is accompanied by a spreading apart of the iso-range ellipses as the iso-range lines are closer together for target 1409 than for target 1403. This phenomonon is equivalent to a loss or dilution of range resolution caused by a change in the scale factor between distance and time delay. The simple corrections described above would not correct for the loss of range resolution.